In the key of C major, making a circle of fifths, I get these chord symbols...

CΔ9 - FΔ9 - bm7♭5 - em7♭9 - am9 - dm9 - G9 - CΔ9

I left the vii chord as just a half-diminished seventh.

I especially wonder about the iii chord. Should it be a minor flat nine?

I know ii-V-I and vi-ii-V-I are jazz basic, but are other segments of the circle using IV, vii, and iii commonly used in jazz?

In the key of C major, making a circle of fifths, I get these chord symbols...

CΔ9 - FΔ9 - Bm7♭5 - Em7♭9 - Am9 - Dm9 - G9 - CΔ9

I left the vii chord as just a half-diminished seventh.

I especially wonder about the iii chord. Should it be a minor flat nine?

I know ii-V-I and vi-ii-V-I are jazz basic, but are other segments of the circle using IV, vii, and iii commonly used in jazz?